Y=(5-x)(7+3x)

Solution for Y=(5-x)(7+3x) equation:

=(5-Y)(7+3Y)

We move all terms to the left:

-((5-Y)(7+3Y))=0

We add all the numbers together, and all the variables

-((-1Y+5)(3Y+7))=0

We multiply parentheses ..

-((-3Y^2-7Y+15Y+35))=0


We calculate terms in parentheses: -((-3Y^2-7Y+15Y+35)), so:

(-3Y^2-7Y+15Y+35)

We get rid of parentheses

-3Y^2-7Y+15Y+35

We add all the numbers together, and all the variables

-3Y^2+8Y+35

Back to the equation:

-(-3Y^2+8Y+35)


We get rid of parentheses

3Y^2-8Y-35=0

a = 3; b = -8; c = -35;
Δ = b2-4ac
Δ = -82-4·3·(-35)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-22}{2*3}=\frac{-14}{6}
=-2+1/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+22}{2*3}=\frac{30}{6}
=5
$